Erosion rate determinator: rocket nozzle

ABSTRACT

In a method for determining and evaluating nozzle erosion rate, an erodingozzle and a non-eroding nozzle are employed in a dual nozzle arrangement to receive a balanced thrust and flow rate from a common solid propellant grain of a solid propellant rocket motor when initially fired. When erosion of the eroding nozzle begins an increase in throat area results and the mass discharged through throat increases thereby causing an imbalance in thrust. The erosion is correlated to the mass flow rate of the solid propellant rocket motor by the mathematical relationships, F 2  P C .sbsb.2 (A t .sbsb.2 +ΔA t .sbsb.2)C F .sbsb.2, wherein F 2  is force, P C .sbsb.2 is chamber pressure, A t .sbsb.2 is throat area, ΔA t .sbsb.2 is change in throat area due to erosion, and C F .sbsb.2 is the thrust coefficient. Thus, the erosion rate of the eroding nozzle is determined and evaluated as a result of the increase of thrust and the flow rate which causes an imbalance in the thrust due to erosion products discharged and a change in value of the A t .sbsb.2 plus ΔA t .sbsb.2.

DEDICATORY CLAUSE

The invention described herein may be manufactured, used, and licensedby or for the Government for governmental purposes without the paymentto me of any royalties thereon.

BACKGROUND OF THE INVENTION

The current method of making measurements by which the erosion rates ofrocket nozzles can be determined and evaluated comprises firing a rocketmotor and exhausting the gases through a test nozzle, measuring thethrust and pressure while firing, and measuring the throat area beforeand after firing. By this method any erosion occurring during theignition transients are not detectable due to ringing of the gaugingsystems.

A device by which the erosion rates of rocket nozzles can be moreprecisely measured and evaluated would be a significant contribution tothe art of nozzle evaluation and design to performance standards.

Therefore, an object of this invention is to provide a device whichenables an initial thrust, to be balanced as compared to a non-erodingnozzle, regardless of any pressure transients, so that the start oferosion is readily detectable.

SUMMARY OF THE INVENTION

A solid propellant rocket test motor is provided two nozzles that areequal in throat area and expansion in a test set-up to determine erosionand erosion rate based on a change in thrust. Nozzle No. 1 is made ofcarbon or molybdenum or other materials which do not erode. Nozzle No. 2is made of eroding materials selected from composites of phenolicsfilled with glass, asbestos, or metals which erode during rocket motoroperation.

During a test set-up, at the initial conditions, flow through eachnozzle is equal; thus, thrust is balanced. As erosion starts there is animbalance in thrust. The test motor has fixtures which provides lugs orsupports which allows thrust measurement in line with the gas flow.Pressure gauges are attached to the solid propellant rocket test motorto measure pressure versus time within the motor. Thus, the thrust andpressure are measured simultaneously. The coefficients of thrust (C_(F))or coefficients of force are equal at initial conditions and duringburning regardless of the change of throat area. Since C_(F) is constantand the motor pressure is the same for both nozzles the throat areachange for the eroding nozzle can be correlated to the motor pressure.The relationships of mass discharge at any time (T)=M=P_(C) A_(t)(total)C_(D), and Areas of nozzles=A_(t) (total)=A_(t).sbsb.1+A_(t).sbsb.2 +ΔA_(t).sbsb.2, wherein M is mass rate of flow, P_(C) ischamber pressure, C_(D) is coefficient of discharge, A_(t1) is throatarea of non-eroding nozzle, A_(t).sbsb. 2 is throat area of erodingnozzle, ΔA_(t).sbsb.2 is change in throat area of eroding nozzle, andA_(t) (total) is total throat areas of non-eroding and eroding nozzle.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a diagramatic view of a horizontally mounted solid propellantrocket motor test vehicle including dual nozzles with matched throatdiameters of a non-eroding nozzle and an eroding nozzle.

FIG. 2 is a diagramatic view of a pendulous mounted $ solid propellantrocket motor test vehicle including dual nozzles with matched throatdiameter of a non-eroding nozzle and an eroding nozzle.

DESCRIPTION OF THE PREFERRED EMBODIMENT

A device by which the erosion rate of a rocket nozzle is more preciselymeasured and evaluated comprises a mounted solid propellant rocket testmotor that is fitted with dual nozzles that are equal in throat area andexpansion. One of the nozzles is constructed of a non-eroding materialand the other nozzle is constructed of an eroding material. Thenon-eroding nozzle No. 1 is made of carbon or molybdenum or othermaterials which do not erode. The other nozzle No. 2 is made ofcomposites such as phenobics filled with glass, asbestos, or may be madeof metals which erode during rocket motor operation.

The test motor is provided with fixtures such as lugs or supports whichallows thrust measurement in line with the gas flow during motorburning. Pressure gauges attached to the motor measure pressure versustime within the rocket motor.

Since the rocket nozzles are equal in throat area and expansion, atinitial conditions flow through each nozzle is equal, thus thrust isbalanced. As erosion start there is an imbalance in thrust, and sincethrust and pressure are measured simultaneously, the difference inthrust is due only to the erosion and is not masked by burning ratechanges or burning surfaces of the propellant.

In further reference to the drawing, FIG. 1 depicts a diagramatic viewof a device 10 by which the erosion rates of a rocket nozzle isprecisely measured and evaluated. The device 10 comprises a rocket motorcase 12 containing a solid propellant grain 14 and fitted with anon-eroding nozzle 16 (without an expansion cone) with a throat areaA_(t).sbsb.1 and an eroding nozzle 18 (without an expansion cone) with athroat area A_(t).sbsb.2. Support lugs 20 retain the rocket motor inplace during firing and allows thrust measurement in line with the gasflow. Pressure or force gauges 22 are attached to the lugs or the rocketmotor case to measure pressure versus time within the rocket motor. Thethroat diameter areas, designated A_(t).sbsb.1 and A_(t).sbsb.2 fornozzles 16 and 18 respectively, are equal before erosion; that is,A_(t).sbsb.1 =A_(t).sbsb.2 initially. A_(t).sbsb.2 for eroding nozzle isgreater after eroding; that is, A_(t).sbsb.2 +ΔA_(t).sbsb.2>A_(t).sbsb.1. Nozzle 18 throat area is shown with indicated erosionpattern.

In further reference to the drawing, FIG. 2 depicts a diagramatic viewof a pendulous mounted solid propellant motor test vehicle which is adevice 30 by which the erosion rate of a rocket nozzle is preciselymeasured and evaluated. The device 30 comprises a rocket motor case 32containing a solid propellant grain 34. A tee shaped (T) configurationalpipe fixture 35 is shown connected to the rocket motor case with anon-eroding nozzle 36 (without an expansion cone) with a throat area ofA_(t).sbsb.1 and an eroding nozzle 38 (without an expansion cone) with athroat area A_(t).sbsb.2 mounted therein. A support member 37 providesthe means for mounting the solid propellant rocket motor test vehicle 30and balancing the rocket motor test vehicle on a pendulum. Thrust orforce gauge 39 is attached to the rocket motor case to measure pressureversus time during the rocket motor operation. The throat diameterareas, designated A'_(t).sbsb.1 and A'_(t).sbsb.2 for nozzles 36 and 38respectively, are equal; that is, A'_(t).sbsb.1 =A'_(t).sbsb.2initially. As noted for embodiment 30, as erosion starts in erodingnozzle 38 there is an imbalance in thrust, and since thrust and pressureare measured simultaneously, the difference in thrust is due only to theerosion and is not masked by burning rate changes or burning surfaces ofthe propellant.

The pendulous mounted solid propellant rocket motor test vehicle isbalanced by determining the balance point of the test vehicle prior totesting. Any imbalance due to nozzle erosion is detected by forcegauges. Erosion is correlated to mass flow through the rocket nozzle.

The following mathematical relationship will provide a betterunderstanding of how the area change for an eroding nozzle can becorrelated to motor pressure. For example, mass flow rate (M₁ and M₂)relate to non-eroding nozzle and eroding nozzle respectively, where massflow rate M₁ =P_(C).sbsb.1 A_(t).sbsb.1 C_(D).sbsb.1 and M₂=P_(C).sbsb.2 A_(t).sbsb.2 C_(D).sbsb.2, and wherein P_(C).sbsb.1 andP_(C).sbsb.2 are chamber pressures, A_(t).sbsb.1 and A_(t).sbsb.2 aretotal nozzle throat areas, and C_(D).sbsb.1 and C_(Ddi) 2 arecoefficients of discharge. Also, F₁ and F₂ and C_(F).sbsb.1 andC_(F).sbsb.2 can be substituted for M₁ and M₂ and C_(D).sbsb.1 andC_(D).sbsb.2 respectively wherein F stands for force; thus, ##EQU1##Therefore, when A_(t).sbsb.1 does not erode, the initial conditions are:A_(t).sbsb.1 =A_(t).sbsb.2, P_(C).sbsb.1 =P_(C).sbsb.2, C_(D).sbsb.1=C_(D).sbsb.2, F₁ =F₂, and C_(F).sbsb.1 =C_(F).sbsb.2 ; also, whenA_(t).sbsb.2 erodes, the conditions during erosion are: A_(t).sbsb.2>A_(t).sbsb.1, P_(C).sbsb.1 =P_(C).sbsb.2, F₂ >F₁ and C_(F).sbsb.1 32C_(F).sbsb.2 (with no expansion cone). Since F₂ >F₁ when erosion occurs,and F₂ -F₁ =ΔF₂, ΔF₂ is thus measured; therefore, it follows that ΔF₂=P_(C).sbsb.1 (A_(t).sbsb.2 -A_(t).sbsb.1 +ΔA_(t).sbsb.2)=P_(C).sbsb.1(O+ΔA_(t).sbsb.2)=P_(C).sbsb.1 ΔA_(t).sbsb.2 ; when eroding,A_(t).sbsb.2 =A_(t).sbsb.1 +ΔA_(t).sbsb.2 ; (also, A_(t).sbsb.2>A_(t).sbsb.1, when eroding), and the measured thrust is equal toP_(C).sbsb.1 (A_(t).sbsb.2 -A_(t).sbsb.1) =P_(C).sbsb.1 l ΔA_(t).sbsb.2.Since P_(C).sbsb.1 =P_(C).sbsb.2, A_(t).sbsb.1 =A_(t).sbsb.2(initially), ##EQU2## The mass discharge rate at any time (T)=M=P_(C)A_(t) (total) C_(D), and A_(t) (total)=A_(t).sbsb.1 +A_(t).sbsb.2+ΔA_(t).sbsb.2. Erosion is then correlated to mass flow rate of themotor. The flow rate through the eroding nozzle is P_(C) (A_(t).sbsb.2+ΔA_(t).sbsb.2) C_(D) at any time (T). Also, erosion is correlated tomass flow rate of the rocket motor at any time (T) by the relationshipF₂ =P_(C).sbsb.2 (A_(t).sbsb.2 +ΔA_(t).sbsb.2) C_(F).sbsb.2.

The rate of change of thrust is linear with the rate of change in area;therefore, the total erosion and erosion rate at any time (T) ismeasured, and the total erosion and erosion rate through the totalaction time of the rocket is also measured.

It is important that the erosion rate determinator of this invention beprovided with a nozzle without an expansion cone section as illustratedin the drawing and as further emphasized now. C_(F).sbsb.1 =C_(F).sbsb.2only when the expansion ratios are equal. With an expansion cone ofequal dimensions, C_(F).sbsb.1 =C_(F).sbsb.2 initially; however, aserosion takes place the expansion ratio changes; therefore, C_(F).sbsb.1=C_(F).sbsb.2 is not equal. When there is no expansion cone the ratioalways has a value of one, therefore, C_(F).sbsb.1 always equalsC_(F).sbsb.2. Hence when the nozzle includes an expansion cone there isan error in the measured thrust as erosion takes place, but with noexpansion cone the measurement of the unbalanced thrust is a truerepresentation. C_(F) is a function of γ, P's and A's where γ is a gasproperty which does not change, P's are pressure relationships which ifchanged, changes proportionally constant and the A's are areas whoseexpansion ratios are constant; therefore, C_(F) for both nozzles remainsconstant through the firing. Expansion ratio is defined as the area ofthe exit plane (A exit plane) of the nozzle over the area of the throat(A throat). A nozzle with no expansion cone has an expansion ratio ofone since the exit plane and the throat area are the same; i.e.,##EQU3##

I claim:
 1. A method for the determination and the evaluation of theerosion rate of a rocket nozzle, said method comprising: (i) providing afirst nozzle constructed of carbon, or molybdenum or other non-erodingmaterial and designed to a predetermined coefficient of thrustC_(F).sbsb.1 and area of throat A_(t).sbsb.1 ;(ii) providing a secondnozzle constructed of components of phenolics filled with glass orasbestos or an eroding metal material and designed to a predeterminedcoefficient of thrust C_(F).sbsb.2 and area of throat A_(t).sbsb.2 saidC_(F).sbsb.2 equal to said C_(F).sbsb.1 and said A_(t).sbsb.1 equal tosaid A_(t).sbsb.2 ; (iii) providing a rocket motor comprising a rocketmotor case with a solid propellant grain contained within said rocketmotor case, said rocket motor case adapted for attachment of said firstnozzle and said second nozzle in a dual nozzle arrangement whereby saidsolid propellant grain when fired discharges products of combustion atan equal rate of force F₁ and F₂ through each of said nozzles initially,and when said A_(t).sbsb.2 of said second nozzle erodes, said F₂ isgreater than said F₁ ; (iv) fitting said rocket motor case containingsolid propellant grain with said first nozzle and said second nozzle toprovide a balanced thrust and flow rate of said products of combustionat initial firing of said propellant grain; (v) providing means formeasuring thrust and pressure simultaneously; and (vi) firing said solidpropellant grain to generate products of combustion to achieve a massdischarge rate at any time (T) equal to M=P_(C) A_(t) (total)C_(D)),wherein C_(D) is coefficient of discharge, A_(t) total equalsA_(t).sbsb.1 +A_(t).sbsb.2 +ΔAt₂, and wherein erosion is correlated tomass flow rate of said solid rocket motor at any time (T) by therelationship F₂ P_(C).sbsb.2 (A_(t).sbsb.2 +ΔA_(t).sbsb.2)C_(F).sbsb.2wherein P_(C).sbsb.2 is chamber pressure, A_(t).sbsb.2 is throat area,ΔA_(t).sbsb.2 is change in throat area due to erosion, and C_(F).sbsb.2is the thrust coefficient, and the erosion rate of said eroding nozzleis determined and evaluated as a result of the increase of thrust andflow rate which results in an imbalance because of erosion products andchange in value of said A_(t).sbsb.2 plus ΔA_(t).sbsb.2.
 2. The methodof claim 1 wherein said rocket motor case is open at both ends andwherein said first nozzle of a non-eroding material is attached on oneend of said rocket motor case and wherein said second nozzle of aneroding material is attached on the opposite end of said rocket motorcase.
 3. The method of claim 1 wherein said rocket motor case is open atone end and closed at the opposite end, and wherein said nozzles aremounted in a tee shaped configurational pipe fixture with said firstnozzle of a non-eroding material and said second nozzle being attachedin said tee shaped configurational pipe fixture for discharging saidproducts of combustion in opposite directions through each of saidnozzles, and wherein said tee shaped configurational pipe fixture isattached to said rocket motor case for directing said products ofcombustion to achieve a balanced thrust and flow rate of said productsof combustion at initial firing of said propellant grain.